oleh pn. chuang bee eng sm teknik batu pahat
DESCRIPTION
LINES AND PLANES IN THREE DIMENSIONS. OLEH PN. CHUANG BEE ENG SM TEKNIK BATU PAHAT. ACTIVITY 1 : TO IDENTIFY THE PLANE. G. H. E. F. D. C. A. B. PLANE AT THE TOP :. PLANE EFGH. G. H. E. F. D. C. A. B. PLANE ON THE LEFT :. PLANE ADHE. G. H. E. F. D. C. A. B. - PowerPoint PPT PresentationTRANSCRIPT
OLEH
PN. CHUANG BEE ENG
SM TEKNIK BATU PAHAT
AB
CD
E F
GH
PLANE AT THE TOP : PLANE EFGH
ACTIVITY 1 : TO IDENTIFY THE PLANE
AB
CD
E F
GH
PLANE ON THE LEFT : PLANE ADHE
AB
CD
E F
GH
PLANE IN THE FRONT : PLANE ABFE
AB
CD
E F
GH
PLANE AT THE BACK : PLANE DCGH
AB
CD
E F
GH
PLANE AT THE BOTTOM: PLANE ABCD
AB
CD
E F
GH
PLANE ON THE RIGHT : PLANE BCGF
ON TOP OF THE RED DOT
TO THE RIGHT OF THE RED DOT
IN FRONT OF THE RED DOT
AT THE BACK OF THE RED DOT
THE LOCATION OF THE POINT
AT THE BOTTOM OF ….
ON THE TOP OF ….
AT THE BACK OF ….
IN FRONT OF ….
TO THE LEFT OF ….
TO THE RIGHT OF ….
ACTIVITY 2 : TO DETERMINE THE LOCATION OF A POINT
A B
CD
EF
GH
POINT TO THE LEFT OF F :
POINT E
POINT G
POINT AT THE BOTTOM OF F :
POINT AT THE BACK OF F :
POINT TO THE RIGHT OF D :
POINT ON TOP OF D :
POINT IN FRONT OF D :
POINT B
POINT C
POINT H
POINT A
ANGLE BETWEEN A LINE AND A PLANE
A
BC
LINE
PLANE
BA
CD
E F
Orthogonal projection
Normal
H G
Activity 3 :To Identify The Angle Between Line And Plane
The line draw from G and perpendicular to the plane ABCD is call normal
The line lies on the plane ABCD which joint the point A to the line GC is known as the orthogonal projection of line AG on the plane ABCD.
The angle between the line AG and the orthogonal projection, AC is the angle between the line AG and the plane ABCD that is GAC.
BA
CD
E F
H G
ACTIVITY 3 : To Identify The Angle Between A Line And A Plane
AG C
Angle between the line AG and the plane ABCD
At the bottom
Name the angle between the line AG and the plane ABCD
Normal
Orthogonal projection
Example 1a
= GAC.
EXAMPLE 1(b)
BA
CDE
H G
F
Diagram 1(b)
Diagram 1b shows a cuboid ABCDEFGH. Name the angle between the line HB and the plane ABCD.
Diagram 2(a) shows a cuboid, ABCDEFG. Find the angle between the line AH and the plane DCGH.
ACTIVITY 4 :
To find the angle between a line and a plane
Example 2(a)
5cm
BA
CD
E
H G
F
4cm
12cm
Diagram 2a
5cm
Draw the line AH and shade the plan DCGH in diagram 2a.
1.
SolutionsStepsNo
A
CD
E
H G
F
5cm
4cm
12cm
BDiagram 2a
Diagram 2a shows a cuboid, ABCDEFG. Find the angle between the line AH and the plane DCGH.
No Steeps Solutions
2 Use the method you have learned in activity 3, identify the angle between the line AH and the plane DCGH
HA
back
D
5cm
BA
CDE
H G
F
4cm
12cm
No Steps Solutions
3 Refer to the points you have obtained in steep 2 (point A, H, D), complete the ∆ AHD. Mark
AHD. Mark the right angle,
HDA. Transfer out the
∆ AHD.
H
DA
5cm
4cm
A H D
BA
CDE
H G
F
12cm
No Steps Solutions
4 With the information given in the question, label the length of the sides of ∆ AHD. At least the length for 2 sides must be known. Use Pythegoras Theorem if necessary.
H
DA
5 cm
4 cm
5cm
BA
CDE
H G
F
4cm
12cm
No Steps Solutions
6 Mark,- the opposite side, AD asT- the adjacent side, HD as S
H
DA
5 cm
4 cm
S
T
5cm
BA
CDE
H G
F
4cm
12cm
No Steps Solutions
6 Use the tangent formula to
calculate AHD.
Remember, use-The sine formula, if O and H were
known
- The cosine formula, if A and H
were known
-The tangent formula, if O and A
were known
Tan AHD =
AHD = tan -1
AHD = 38040’
– TOAA
O T
- SOH
H
O S
– CAHH
A C
5
4
5
4
5cm
BA
CD
E
H G
F
4cm
12cm
example 2 (b)
Diagram 2b shows a cuboid,ABCDEFGH. Calculate the angle between the line HB and the plane BCGF
A B
CD
E F
GH
4 cm
12 cm
3 cm
Diagram 2b
ANGLE BETWEEN TWO PLANES
ACTIVITY 5 : To Identified The Angle Between Two Planes
A
E
B
CD
H G
F
Diagram 3a
Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane AGH and the plane ABCD
1.DRAW 3 LINES
EXAMPLE 3(a)
BA
CDE
H G
F
Diagram 3a
Bottom
2.Mark the location (direction) of the plane ABCD at the bottom of the first line to the left.
ACTIVITY 5 : To Identified The Angle Between Two Planes
Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD
BA
CDE
H G
F
Diagram 3a
A
Bottom
3.Refer to the plane, AGH, identify the points which touch the plane, ABCD and write it at the middle line.
ACTIVITY 5 : To Identified The Angle Between Two Planes
Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD
BA
CDE
H G
F
Diagram 3a
AH / G
Bottom
3.Refer to the plane, AGH, identify the point which does not touch the plane, ABCD and write it at the first line to the left.
ACTIVITY 5 : To Identified The Angle Between Two Planes
Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD
BA
CDE
H G
F
Diagram 3a
AH/G
Bottom
5.Between the point H and G, point which is nearer to point A or located on the same plane as point A will be choosen. Point which is not choosen will be earased.
ACTIVITY 5 : To Identified The Angle Between Two Planes
Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD
BA
CDE
H G
F
Diagram 3a
AH
Ke Bawah
5.Between the point H and G, point which is nearer to point A or located on the same plane as point A will be choosen. Point which is not choosen will be earased.
ACTIVITY 5 : To Identified The Angle Between Two Planes
Diagram 3a shows a cuboid, ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD
BA
CDE
H G
F
Diagram 3a
AH
Bottom
D
6. Identify the point which is located at the bottom of the point H ( )and write it on the first line to the right.Diagram 3a shows a cuboid,
ABCDEFGH. Name the angle between the plane, AGH and the plane, ABCD
ACTIVITY 5 : To Identified The Angle Between Two Planes
BA
CDE
HG
F
Diagram 3a
Bottom
AH D
7. In the diagram 3a, complete the ∆ HAD and mark the HAD
Angle between the plane, AGH and the plane, ABCD = HAD
ACTIVITY 5 : To Identified The Angle Between Two Planes
EXAMPLE 3(b)
Diagram 3b
E5cm
BA
CD
H G
F
4cm
12cm
Diagram 3b shows a cuboid with horizontal rectangle base ABCD. Name the angle between the plane ACH and the plane CDHG
THANK YOU